LMFDB - Group of Dirichlet characters of modulus 1850

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1850)

pari: g = idealstar(,1850,2)

Character group

sage: G.order() pari: g.no
Order	=	720
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1850}(1777,\cdot)$, $\chi_{1850}(1001,\cdot)$

First 32 of 720 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{1850}(1,\cdot)$	1850.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1850}(3,\cdot)$	1850.ch	180	no	$-1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{1850}(7,\cdot)$	1850.bn	36	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1850}(9,\cdot)$	1850.bz	90	no	$1$	$1$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{1850}(11,\cdot)$	1850.bl	30	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1850}(13,\cdot)$	1850.cc	180	no	$1$	$1$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{47}{60}\right)$
$\chi_{1850}(17,\cdot)$	1850.cf	180	no	$1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{49}{60}\right)$
$\chi_{1850}(19,\cdot)$	1850.ce	180	no	$-1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1850}(21,\cdot)$	1850.ca	90	no	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1850}(23,\cdot)$	1850.bw	60	no	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1850}(27,\cdot)$	1850.bv	60	no	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1850}(29,\cdot)$	1850.by	60	no	$-1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1850}(31,\cdot)$	1850.bi	20	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1850}(33,\cdot)$	1850.cg	180	no	$-1$	$1$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{60}\right)$
$\chi_{1850}(39,\cdot)$	1850.ce	180	no	$-1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1850}(41,\cdot)$	1850.ca	90	no	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1850}(43,\cdot)$	1850.g	4	no	$1$	$1$	$-i$	$-i$	$-1$	$-1$	$-1$	$1$	$-i$	$-1$	$-1$	$i$
$\chi_{1850}(47,\cdot)$	1850.bu	60	no	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1850}(49,\cdot)$	1850.bc	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1850}(51,\cdot)$	1850.y	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-1$
$\chi_{1850}(53,\cdot)$	1850.cg	180	no	$-1$	$1$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{1850}(57,\cdot)$	1850.br	36	no	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1850}(59,\cdot)$	1850.ce	180	no	$-1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1850}(61,\cdot)$	1850.cd	180	no	$-1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{1850}(63,\cdot)$	1850.bu	60	no	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1850}(67,\cdot)$	1850.ch	180	no	$-1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{1850}(69,\cdot)$	1850.ce	180	no	$-1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1850}(71,\cdot)$	1850.bs	45	no	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1850}(73,\cdot)$	1850.be	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1850}(77,\cdot)$	1850.ch	180	no	$-1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{60}\right)$
$\chi_{1850}(79,\cdot)$	1850.ce	180	no	$-1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1850}(81,\cdot)$	1850.bs	45	no	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{15}\right)$

Click here to search among the remaining 688 characters.

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$1850$
Structure	\(C_{4}\times C_{180}\)
Order	$720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{1850}(1,\cdot)\)	1850.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1850}(3,\cdot)\)	1850.ch	180	no	\(-1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{1850}(7,\cdot)\)	1850.bn	36	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1850}(9,\cdot)\)	1850.bz	90	no	\(1\)	\(1\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{1850}(11,\cdot)\)	1850.bl	30	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1850}(13,\cdot)\)	1850.cc	180	no	\(1\)	\(1\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{1850}(17,\cdot)\)	1850.cf	180	no	\(1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)
\(\chi_{1850}(19,\cdot)\)	1850.ce	180	no	\(-1\)	\(1\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1850}(21,\cdot)\)	1850.ca	90	no	\(1\)	\(1\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1850}(23,\cdot)\)	1850.bw	60	no	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1850}(27,\cdot)\)	1850.bv	60	no	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1850}(29,\cdot)\)	1850.by	60	no	\(-1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1850}(31,\cdot)\)	1850.bi	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1850}(33,\cdot)\)	1850.cg	180	no	\(-1\)	\(1\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)
\(\chi_{1850}(39,\cdot)\)	1850.ce	180	no	\(-1\)	\(1\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1850}(41,\cdot)\)	1850.ca	90	no	\(1\)	\(1\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1850}(43,\cdot)\)	1850.g	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)
\(\chi_{1850}(47,\cdot)\)	1850.bu	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1850}(49,\cdot)\)	1850.bc	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1850}(51,\cdot)\)	1850.y	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-1\)
\(\chi_{1850}(53,\cdot)\)	1850.cg	180	no	\(-1\)	\(1\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{1850}(57,\cdot)\)	1850.br	36	no	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1850}(59,\cdot)\)	1850.ce	180	no	\(-1\)	\(1\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1850}(61,\cdot)\)	1850.cd	180	no	\(-1\)	\(1\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{1850}(63,\cdot)\)	1850.bu	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1850}(67,\cdot)\)	1850.ch	180	no	\(-1\)	\(1\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{1850}(69,\cdot)\)	1850.ce	180	no	\(-1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1850}(71,\cdot)\)	1850.bs	45	no	\(1\)	\(1\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1850}(73,\cdot)\)	1850.be	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1850}(77,\cdot)\)	1850.ch	180	no	\(-1\)	\(1\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{1850}(79,\cdot)\)	1850.ce	180	no	\(-1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1850}(81,\cdot)\)	1850.bs	45	no	\(1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 720 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.